A Calculation Method of Parameter-dependent LMIs on Nonlinear Affine Basis

Abstract

A calculation method of polynomially parameter-dependent LMIs (Linear Matrix Inequalities) is proposed by employing Bernstein polynomial basis. Based on the fundamental properties of the Bernstein basis, it is shown that the parameter-dependent LMI conditions are systematically transformed to standard LMI conditions, and the finite division of the parameter range enables to treat the necessary and sufficient condition with arbitrary resolution and precision. The features of the proposed calculation method are illustrated with numerical examples.